Question

Can a polyhedron have 11 faces, 22 Vertices and 33 edges? ​

Answer 1

No, a polyhedron cannot have 11 faces, 22 Vertices, and 33 edges

For any of the 3-dimensional figure is can be the polyhedron if and only if the faces, vertices, and edges of the polyhedron follow the following rule:

V-E+F = 2

and in the question, we have given the faces, vertices, and edges as:

V = 22

E = 33

F = 11

Let us take the LHS of the formula

• V-E+F
• 22-33+11
• 33-33
• 0

it is clear that 0 is not equal to 2

So, any figure with these number of faces vertices, and edges can never be a polyhedron